The plots of intensity $(I)$ versus wavelength $(\lambda)$ for three black bodies at temperatures $T_1, T_2$ and $T_3$ respectively are as shown. Their temperatures are such that:

If $\lambda$ denotes the wavelength at which the radiative emission from a black body at a temperature $T$ is maximum, then

$A$ black body is at a temperature of $5760 \ K$. The energy of radiation emitted by the body at wavelength $250 \ nm$ is $U_1$,at wavelength $500 \ nm$ is $U_2$ and that at $1000 \ nm$ is $U_3$. Wien's constant,$b = 2.88 \times 10^6 \ nm \ K$. Which of the following is correct?

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \, nm$. The radiation intensity of the star is (Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$, Wien's constant $b = 2898 \, \mu m K$).

Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of $6000\,K$. Maximum intensity is emitted at a wavelength of about $4800\,\mathring{A}$. If the sun was cooled down from $6000\,K$ to $3000\,K$,then the peak intensity would occur at a wavelength of ........ $\mathring{A}$.